Seite - 94 - in The Austrian Business Cycle in the European Context

94 (45) w(n)=-- ---n---2 (N1 I N-11) N-1 2 2 with N being the length of the filter (e.g. in quarters) and n being an integer number with values 0 :s; n :s; N - 1 which is augmented successively. The values are ranging from numbers close to 1, indicating a strong comovement within the observed frequency range, to 0 in the case of no comovement. It is clear that time series which are closely defined to the reference series (Austrian GDP or GVA) show a higher coherence than others. It is therefore more informa- tive to concentrate on the others. Compared across all three filtering methods, the Austrian manu- facturing sector shows the largest coherence values, as expected on theoretical grounds. In the first-order-difference case, around 50 percent of the variability observed between 6 and 32 quarters can be explained by co-moving variability. For HP- and BK-filtered data, this amount rises to approximately 75 percent. Such high lin- ear comovement is somewhat biased by the fact that this sector is part of the reference series (autGVAex), but it is also consistent with theory which suggests that manufacturing is strongly subject to business cycle variations 107. Considering the rest of the Austrian sectors, the construction indus- try's comovement at the business cycle frequencies with autGVAex is relatively high in the first-order-difference case, at 0.32. The results of the HP- and BK-filtered data do not confirm this, with a value of 0.21 in both cases. Again, weather effects could play a substantial role. The Austrian sector with the lowest coher- ence is the sector of financial intermediation services and real es- •07 Indeed, many studies use manufacturing output or industrial production as ad- hoc reference series for their business cycle analysis. Examples are Artis - Kro/zjg - Toro (2004), Vijselaar -Albers (2001) or Brandner -Neusser (1992).